Scale-up effects on flow patterns in the high shear mixing of ......Keywords: high shear mixer,...

Cavinato, M., Artoni, R., Bresciani, M., Canu, P., Santomaso, A.C. Scaleup effects on flow patternsin the high shear mixing of cohesive powders (2013) Chemical Engineering Science, 102, pp. 19.

DOI: 10.1016/j.ces.2013.07.037

Scale-up effects on flow patterns in the high shear mixing ofcohesive powders

Mauro Cavinato, Riccardo Artonib, Massimo Brescianic, Paolo Canua, Andrea C. Santomasoa,*

aAPTLab - Advanced Particle Technology Laboratory, Università di Padova, Dipartimento di Ingegneria Industriale, via Marzolo 9, 35131 Padova, ItalybL’UNAM, IFSTTAR Route de Bouaye, CS4, 44344 Bouguenais Cedex, FrancecResearch Center Pharmaceutical Engineering GmbH, Inffeldgasse 13, 8010 Graz, Austria

*Corresponding author: [email protected]

AbstractProcessing of granular material often requires mixing steps in order to blend cohesive powders,distribute viscous liquids into powder beds or create agglomerates from a wet powder mass. For thisreason, using bladed, high-speed mixers is frequently considered a good solution by many types ofindustry. However, despite the importance of such mixers in powder processing, the granular flowbehavior inside the mixer bowl is generally not totally understood. In this work extensiveexperimentation was performed comparing the behavior of a lab-scale mixer (1.9 l vessel volume)to that of a pilot-scale mixer (65 l vessel volume) with a mixture of some pharmaceutical excipients(e.g. lactose, cellulose). The aim was to propose a new and more detailed method for describing thecomplex powder rheology inside an high shear mixer using impeller torque, current consumptionand particle image velocimetry (PIV) analysis. Particularly, a new dimensionless torque number isproposed for the torque profile analysis in order to isolate the contributions of mass fill and bladeclearance at the vessel base. Impeller torque and motor current consumption were integrated withPIV to obtain more detailed information about the surface velocity and flow pattern changes in thepilot-scale mixer. Mass fill resulted to be one of the most critical variables, as predicted by thetorque model, strongly affecting the powder flow patterns. An additional mixing regimes wasfurthermore defined according to the observation of the surface velocity of the powder bed.

Keywords: high shear mixer, cohesive powders, scale-up, mixing regimes

1 IntroductionHigh shear mixers, also known as high intensity mixers (Paul et al., 2003), are widely used for thepowder processing. They can be used for simple mixing, in particular of cohesive materials, sincethey exert a high local shear on the powder which breaks down the small aggregates (Harnby,1997), or for more complex operations which involve both solids and liquids. For example in a wetgranulation process, a high shear mixer can promote a good liquid dispersion and properconsolidation of the product, in order to obtain aggregates with useful structural forms, improvedflow properties and reduced segregation propensity (Litster et al., 2004). They are constituted by abowl and a centrally mounted impeller rotating about a vertical or an horizontal axis. For the case

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http://dx.doi.org/10.1016/j.ces.2013.07.037


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with vertical axis, which is studied presently, the impeller can be top- or bottom-driven. Despite theimportance of this type of mixers in many industrial processes (Knight et al., 2001), the granularflow behaviour inside the vessel (i.e. how the motion of the powder within the mixer is induced bythe impeller) is currently not totally understood. Different techniques have been used in order tocarry out a description of the powder flow within the mixer. Techniques such as positron emissionparticle tracking (PEPT) and particle imaging velocimetry (PIV) give a direct visualization of theflow patterns within the bulk of powder and at the boundaries (typically the free surface)respectively. Also other experimental methods such as thermal tracer method (Saberian, 2002) orsimulation techniques such as the discrete element method (DEM) (Stewart et al., 2001,Chandratilleke et al., 2010, 2012, Radl et al., 2012, Remy et al., 2010) have been used with the aimof observing and understanding the internal flow patterns in powder mixing. PEPT technique(Wellm, 1997) and high-speed imaging (Litster et al., 2002, Nilpawar et al., 2006) in particular bothconfirmed that the powder mass within the vessel can exhibit a toroidal vortex motion consisting inan outward motion in the lower regions of the mixer and a inward motion in the upper regions, withlifting at the wall and falling close to the axis of the mixer (Salman et al., 2007). However resultsobtained with high speed imaging by Plank et al. (2003) suggest that the powder bed dynamics canbe more complex. Authors have found that small increases in fill level can significantly decrease thepowder velocity at the surface. At large scale mixers, they have observed that the surface wasstagnant approximately 1/3 of each impeller revolution.

Amperage as well as motor power consumption, impeller torque and motor slip have beenfrequently monitored as indirect effects of the mixing process on the mixer. Particularly, powerconsumption and impeller torque have been used to identify how the flow patterns in a mixerdepend on the geometric configuration (impeller shape as well as bowl shape) and the impellerspeed (e.g. Paul et al., 2003; Dareliusa et al., 2007). In particular Knight et al. (2001) developed amodel for predicting impeller torque in a high shear mixer. They represented the effect of the massof powder M and the bowl radius R using a dimensionless torque group T/MgR as a function of theimpeller Froude number and changed several operating conditions: impeller geometry, impellershape, mass fill, bowl diameter, impeller clearance and powder size distribution. They obtained agood correlation between the proposed model and the experimental data.

The geometrical similitude has been frequently identified as an essential prerequisite forscaling-up powder mixers (Litster et al., 2002; Fan et al., 1990), and should be in principle the firstto be assured among kinematic and dynamic ones. The design of industrial mixers neverthelessvaries from manufacturer to manufacturer and might present differences in bowl proportions andimpeller shape at different scales (i.e. variations in blade angle and shape of the blades). Also fillinglevel of the bowl should be scaled according to geometric rules. However, while the quantity ofmaterial processed at the laboratory stage usually tends to be minimized in order to reduce wastesand costs, at industrial level it is maximized in order to increase the productivity (Litster et al.,2002). In practice, the geometric similitude is seldom fully respected. Also the high-shear mixersused in the present research were not geometrically similar. The shape of the small-scale bowl was alittle bit more smoothed in the bottom border (i.e. close to the impeller tip), thus small-scale bladeswere slightly more curved. Moreover small-scale mixer was top-driven, while pilot-scale wasbottom-driven. On the other hand, blade angle was similar for both mixer scales. In the literature thebehavior of free-flowing (Knight et al., 2001) or idealized (spherical) materials (Radl et al., 2012) isoften studied for sake of simplicity. Here an industrial mixture of cohesive powders was used.





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The aim of this work was to propose a more detailed model for the prediction of torque in ahigh shear mixing process of cohesive powders by introducing a modified dimensionless torquenumber as a function of the impeller Froude number and taking into account of the filling ratio ofthe vessel and the impeller clearance at the vessel base, i.e. the distance from bottom wall of thebowl. Among all the operating variables, mass fill resulted to be one of the most critical parametersfor choosing the mixing patterns and shear energy (Paul et al., 2003, Landin et al., 1996a,b) and forthe characteristics of the final products (Mangwandi et al., 2011). Predicting torque with higherlevel of precision can be useful not only because torque quantifies the power required by the motorto move the impeller (i.e. useful for design purposes), but also because it is strongly related to theflow patterns and the motion regimes of the material within the vessel which impact on the mixingefficiency. The new dimensionless number clearly isolated the contribution of the mass fill and theblade clearance at the vessel base. Our own experiments and literature data by Knight et al. (2001)have been used in order to validate the new model, to give a physical meaning to the parameters andto better characterize the flow pattern inside the mixer.

2 Materials and methods

Experiments were performed using a bench-scale and a pilot-scale mixer. The bench-scale mixer(MiPro, 1900 ml vessel volume, ProCepT, Zelzate, Belgium) was top driven (Figure 1) and thepilot-scale mixer (Aeromatic Fielder PMA 65 L, Eastleigh, Hampshire, UK) was bottom driven(Figure 2). Both of the mixers had stainless steel vessels and three bladed impellers. Impeller bladeangle was about 30° for both of them.

Figure 1. Schematic of the bench-scale mixer. Impeller is three bladed, top-driven and equipped with atorque measurement and registration system.

The bench-scale mixer was equipped for measuring the impeller torque while the pilot-scale mixerfor measuring the motor current values. A mixture of some pharmaceutical excipients was used:lactose monohydrate 150 mesh, 73.5% w/w (Lactochem Regular Powder 150 M, Friesland Foods,Zwolte, The Netherlands), microcrystalline cellulose (MCC), 20% w/w (Pharmacel 101, DMVInternational, Veghel, The Netherlands), hydroxypropylmethylcellulose (HPMC), 5% w/w





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(Pharmacoat 603/Methocel E5, Shin-Etsu Chemicals, Niigata, Japan) and croscarmellose sodium,1.5% w/w (Ac-Di-Sol, FMC Biopolymer, Philadelphia, USA). The mass fill was varied between20% and 40% for both the mixers.

Figure 2. Schematic of the pilot-scale mixer: (a) location of the high speed CCD camera and (b) coordinatesystem for the surface velocity measurements tangential direction (tangential velocity) is parallel to the

impeller tip speed; radial direction (radial velocity) is pointing towards the centre of the bowl andperpendicular to the impeller tip speed. The two components belong to a plane which is roughly

perpendicular to the bed surface.

The impeller clearance in the bench-scale mixer was also modified adding one or more annularspacers between the bowl and the mixer closing cup which holds the impeller.Powder flow patterns in the pilot-scale mixer was characterized by measuring the powder surfacevelocity. A high speed camera (FastCam PCI 1000, Photron) at 1000 fps and PIV software writtenin MATLAB were used. Since the surface velocity measurements for the dry mixture could not beacquired for the presence of dust, a very small amount of water (less than 2% w/w of the batch size)was added. The mixture was observed from a sampling port on the top closing cover and the highspeed CCD camera was placed perpendicularly to the moving powder surface as in Figure 2a(closing cover not shown). The coordinate system chosen for the analysis is also shown in Figure2b. 512x240 images were acquired at 200 fps. PIV was performed using the open source MATLABtoolobox MatPIV (Sveen, 2004), adopting an interrogation window shifting technique (Westerweelet al., 1997) in three steps (24x24; 24x24; 12x12) and filtering the velocity field to remove wildvectors.

3 Results and discussion

Knight et al. (2001) measured the impeller torque values during the mixing of sand ofdifferent size fractions in high shear mixers, changing the impeller blade design, rotational speed,fill and bowl size. They represented experimental data by a dimensionless torque number T:





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(1)

where t is the measured torque value (Nm), R is the bowl radius (m), Mtot is the bowl mass capacity (kg) and g is the gravitational constant (9.81 m s-2). For best representing the results obtained using the bench-scale mixer, a new dimensionless torque number has been considered taking into account explicitly the vessel fill ratio, X:

(2)

which is function of X but also of the new parameter . The parameter accounts for the effect ofa “static” contribution, equivalent of a static head which is not a function of the impeller speed, anda “dynamic” contribution, function of the impeller speed:

(3)

where S and D are two constants and FrI is the Froude number related to the impeller speed:

(4)

where ωI is the angular speed (rad s-1) of the impeller. The introduction of X and FrI is one of thenovelties of this study - see for comparison Eq.(1) - and accounts for the effects of the fill ratio andimpeller speed on the distribution of the powder inside the vessel which changes because of thecentrifugal action of impeller rotation and is expected to impact on the measured torque.

The experimental data by Knight et al. (2001) (Figure 3a) can be rescaled according to thenew dimensionless group of Eq.(2) as shown in Figure 3b. The results show that the impeller torquedata points can be fitted by a linear function when they are plotted in the form of the newdimensionless torque number against the square root of the impeller Froude number.Now a static kS and a dynamic kD part, derived from Eq. (2) and Eq.(3), can be clearly separated as follows:

(5)





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(a) (b)Figure 3. Torque profiles (a) obtained by Knight et al., (2001) for different mass fills, using a high shear

mixer with a bowl diameter of 0.30 m, and (b) dependence of the new dimensionless torque number on thesquare root of FrI, impeller torque data presented by Knight et al., (2001).

C is the slope of the master curve which depends on the bowl geometry and mass capacity.The torque profiles obtained using the bench-scale mixer at different blade clearances at the

vessel base (0.5, 2 and 4 mm) and mass fills (20, 30 and 40%) are shown in Figure 4. Eachmeasurement was repeated at least three times and torque profiles resulted to be almost overlyingfor a given mass fill and blade clearance. For this reason, error bars are not visible in Figure 4 sincethey are completely negligible.

Figure 4. Torque profiles obtained using the bench-scale mixer at different mass fills and clearance values.

It can be seen that the fill ratio strongly affects the impeller torque value at different impeller speedsduring the mixing of the dry mixture. In particular it can be noted that for low fill ratios, torque





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profiles can be roughly divided into two parts. At low rotational velocity, impeller torque increaseslinearly with increasing the impeller speed while at higher impeller speed it tends to becomeconstant. For larger fill ratio instead the torque slope variation is roughly constant and the increaseis mostly linear. Especially when the mass fill is 20%, the break point in the torque profilecorresponding to the change in slope can be clearly distinguished. The change in slope occurs at800-900 rpm for the smallest fill ratio and seems to be delayed to higher impeller speed withincreasing the fill ratio. These results slightly differ from the findings of Knight et al. (2001). Theyalso noted that the dependence of torque on impeller speed displayed s-shaped character (i.e.decrease in torque profile slope for impeller speed higher than a critical value) but the degree of s-shaped character slightly increased with increasing the mass fill. This discrepancy might be causedby the different impeller blade design, infact they used an impeller blade angle of 90° for thecomparison between different mass fill instead of 30° blade angle used in the present work. Thisdifference might lead to different flow patterns, thus determining different impeller torque profiles.

The break point in torque profiles in Figure 4 can be explained by considering the resultspresented by Litster et al. (2002). They measured the variation of powder surface velocity duringthe mixing of a similar granular mixture at different rotational speeds. The mixture was composedof lactose monohydrate. According to their results, two mixing regimes can be identified. At lowimpeller speeds, “bumping regime” was observed: powder surface remained horizontal and the bedwas raised as the impeller passed underneath. At higher impeller speeds, “roping regime” wasnoted. The powder flow regime was determined from the well-known toroidal flow pattern and thepowder bed resulted to be more expanded. The transition between the two different regimes wasclearly described by the surface velocity measurements. The velocity values increased linearly withthe impeller speed in the bumping regime. In the roping regime instead, surface velocities are nolonger proportional to the rotational speed of the blades and tend to stabilize around a constantvalue. It is thus suggested that the slope variation in torque profiles in Figure 4 (i.e. break point) canrepresent the transition between the bumping regime and the roping regime. As a matter of fact,impeller torque represents the resistance of the powder to the mixing. Powder bed results to be moreexpanded during the roping regime and vertical turnover is very effective, thus the resistanceexerted from the powder on the impeller blades is expected to be less influenced from the increaseof rotational speed in this case. Moreover, it is suggested that the powder bed expansion can bemore difficult to achieve when fill ratio is higher and more energy (i.e. higher rotational speed)might be required in order to force up the powder and obtain the transition between the two flowregimes. This phenomenon might explain the increase in the rotational speed required to determinethe break point in the torque profiles when mass fill is higher, as reported in Figure 4. Similarconsiderations about the effects of mass fill on the achievement of the roping flow have beenproposed by Litster et al. (2002) in their published work. In addition, Figure 4 shows that changesin the blade clearance determine a smaller variation in the torque profiles compared to the effects ofthe mass fill variation. Particularly, it can be noted that torque values tend to decrease withincreasing the impeller clearance. It is suggested that increasing the impeller clearance mightdecrease the friction between the impeller and the bottom of the bowl. The shape of the profilesseems to be independent on the impeller clearance instead. The model proposed in Eq. (2) was thenused to fit torque profiles in Figure 4. Accordingly three linear master curves were obtained: each ofthem represents a certain impeller clearance and summarizes the effect of the mass fill on theimpeller torque value (Figure 5).





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Figure 5. Dependence of the new dimensionless torque number on the square root of impeller Froudenumber: each of the curves represents an impeller clearance value (bench-scale mixer).

The three master curves in Figure 5 are close to each other but a certain difference in slopeand intercept can be noted. A more considerable difference in slope can be observed between curvesrepresenting 4 mm and 2 mm height. Particularly, the slope of the master curve increases withincreasing the impeller clearance from 2 mm to 4 mm. These results are in agreement with thosepresented by Knight et al. (2001), while the result for the curve representing 0.5 mm clearanceslightly differs.

The effect of the variation of mass fill and impeller clearance on the static term kS can beobserved in Figure 6. The static term kS distinctly depends on the impeller clearance for a givenmass fill. Particularly, kS increases with increasing the impeller clearance. It can be therefore notedthat the higher is the impeller clearance (i.e. impeller distance from the bottom) the weaker is thedependence of kS on the mass fill.

Figure 6. Dependence of the parameter kS in Eq. (5) on the mass fill and the impeller clearance, duringmixing of dry powders at bench-scale.





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As can be seen in Figure 6, kS values corresponding to the highest impeller clearance (4 mm)does not show any dependence on the mass fill. Also the dynamic term kD is plotted and related tothe square root of the impeller Froude number. Figure 7 shows the kD values and the comparisonbetween different impeller clearances and bowl mass fills.

Figure 7. Dependence of the parameter kD in Eq. (5) on the square root of the impeller Froude number: effectof the mass fill X and the impeller clearance during mixing of dry powders at bench-scale.

The variation of the dynamic term kD with the impeller speed mainly depends on the mass fill (seeFigure 7). It is interesting to note that the slope of kD profiles tend to be higher when mass fill islower. A higher slope in kD profile can be correlated with a sharper change in slope of torqueprofiles at lower impeller speed values (see Figure 4): in fact the change in slope in the torqueprofiles was more pronounced when mass fill was lower. As can be observed in Figure 7, anydependence of kD on the impeller clearance can be neglected, since kD profiles at different impellerclearances are almost superimposed for a given mass fill.

Mixing of the same mixture of dry powders was performed using a pilot-scale mixer as well.The results of this first analysis on impeller torque profiles at bench-scale suggested the essentialimportance of mass fill in determining the granular flow behaviour within the mixer bowl. For thisreason, the second analysis was mainly focused on the effects of mass fill variation on the flowpatterns during powder mixing using the pilot-scale mixer. As a first assumption, minimum andmaximum rotational speeds of the pilot-scale mixer were chosen in order to keep the same range ofimpeller tip speed as in the bench-scale mixing. Thus, the range of impeller tip speed was about 2-10 m/s. The impeller tip speed v was calculated using the Eq. (6):

where N is the rotational speed (rpm) and D is the impeller blade diameter (m) (Koller et al., 2010). Accordingly, rotational speed for the pilot-scale mixer results to be lower compared to the bench-scale mixer for a given range of impeller tip speed.





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Motor current values were then measured at different rotational speeds (150-400 rpm) andfor three different mass fills (20, 30 and 40%). Resulting profiles are reported in Figure 8. Eventhough motor current is known to be less accurate than impeller torque for monitoring mixing inbladed mixers, motor current profiles in Figure 8 are here considered as an indication of the load onthe main impeller and qualitatively compared with torque profiles in Figure 4.

Figure 8. Motor current measurements during the mixing of dry powders with the pilot-scale mixer atdifferent rotational speeds (150-400 rpm) and mass fill (20, 30 and 40%).

As can be easily noted from the comparison, the slope of the motor current profiles tends todecrease with increasing the rotational speed. The change in slope is not as sharp as in the torqueprofiles, but still each motor current profile can be ideally divided into two parts characterized bydifferent slopes. Surface velocity measurements were therefore taken in order to get more accurateinformation about the powder flow behaviour and to determine how the transition between bumpingand roping regime is affected by the mass fill variation during the mixing at pilot-scale. A highspeed camera and particle image velocimetry (PIV) software were used. The fluctuation of surfacevelocity in radial and tangential directions during the measurement time and for a given rotationalspeed and mass fill can be effectively described by attractor plots (Figure 9).

As can be noted from the annular shape of attractors in Figure 9a, the surface movementtended to be strongly periodic: while rotating, the bed was locally raised when the impeller bladepassed underneath and, as a consequence, a heap formed with the powder forced to displace fromthe vessel wall to the centre of the bowl. After the blade has passed, the powder bed tended to returnback to its initial position. This phenomenon can be considered as a typical feature of the bumpingregime and determined regular oscillations of the radial and tangential velocity components. It canbe furthermore noted from the attractors plot that this oscillation decreases with increasing therotational velocity and that the tangential component of the velocity is one order of magnitudelarger than the radial one confirming observation by Remy et al. (2010).





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Figure 9. Attractor plot representing the variation of powder surface velocity for the pilot-scale mixer atdifferent mass fills (20, 30 and 40%) and (a) at 150 rpm, (b) 300 rpm and (c) 400 rpm.

Remy et al. (2010) performed simulation studies based on DEM of the mixing process of mono-disperse, cohesionless spheres in a bladed mixer. They found that a three dimensional recirculationconvective zone develops near the front of the impeller blades for low mass fill, promoting a goodvertical and radial mixing. These recirculation zones are strongly related to the heaps observed onthe surface of the bed. At high mass fills, the convective zone is compressed towards the bottom ofthe vessel and the transport of material to the bed surface is limited. Koller et al. (2010)experimentally proved Remy et al. (2010) results by analyzing convective and diffusive propertiesof a binary pharmaceutical powder blend. Using NIR spectroscopy for monitoring the powder-blendcomposition, they demonstrated that for high fill levels diffusive mixing is prevailing and stronglyreduces blending kinetics. However the simulations performed by Remy et al. (2010) were carriedout at low rotational speed (10-20 rpm) and it is likewise important to study what happen at higherrotational speed.





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Figure 10. Variation of surface velocity as a function of impeller rotational speed during the mixing at pilot-scale: (a) variation of mean values and (b) standard deviation.

The description made through the attractor plots can be put on a more quantitative base by plotting the averaged surface velocity and its standard deviation (Figure 10) as a function of impeller speed for the three fill levels considered.

The mean surface velocity (m/s) was calculated using the Eq. (7):

(7)

where and are the radial and tangential velocity component respectively. The standard deviation of the surface velocity was instead evaluated as:

(8)





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As can be seen in Figure 10, mean surface velocity and standard deviation values are clearlyaffected not only by the impeller rotational speed but also by mass fill. Particularly with respect tomass fill, two different behaviours can be observed at 20% mass fill and at 30-40% mass fillrespectively. At 20% mass fill standard deviation profile after a strong initial decrease stabilizes at aminimum value at 250 rpm. At this value of impeller speed the average velocity start to increaseweakly with a sudden increase after 350 rpm. This behaviour suggests that a change in motionregime has occurred within the vessel. Powder flow is therefore likely to be more mono-directionaland to follow the well-known toroidal pattern; hence the roping regime has developed. This idea isconfirmed by considering the radial component of the surface velocity (Figure 11) which, at 20%mass fill, follows the same trend of the standard deviation. It decreases up to 250 rpm and thenstabilizes at around a minimum value.

Figure 11. Average radial velocities at the surface as a function of impeller speed and parametric in the massfill (pilot-scale mixer).

It is suggested therefore that the transition between bumping and roping regime can be described bya decrease of radial velocity and standard deviation values, which reach a minimum value at acritical impeller rotational speed. It can be observed also that the average radial velocity componentis always positive, meaning that the surface dynamics continually leads powder from the wall to thecentre of the vessel. The tangential profile was not considered in the analysis since it is qualitativelyand quantitatively very similar to the mean surface velocity profile of Figure 10a (the tangentialvelocity is one order of magnitude larger than the radial one as can be observed in Figure 9).

At 30 and 40% mass fill the behaviour of the bed seems to deviate from the simple schemebumping/roping regimes typical of 20% mass fill. The mean surface velocity profiles at 30 and 40%mass fill show a maximum value at around 250 rpm, then surface velocity monotonically decreases(40% mass fill) or decreases and stabilizes around a constant value (30% mass fill). As a generalcomment, it can be observed that the mean surface velocity increases lowering the mass fill, withexception at around 250 rpm. Also standard deviation profiles in Figure 10b show different trends.They are similar for 30 and 40% mass fill and initially decrease with increasing impeller rotationalspeed, then increase at 250 rpm and finally stabilizes around a minimum value after 300 rpm. Thedecrease of mean velocity after the transition point at higher mass fills (especially at 40% mass fill)





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can be explained by considering the formation of two ideal mixing layers: a bottom layer whichwraps the area surrounding the impeller, and a top layer which is poorly affected by the bladeconvective motion. With increasing the mass fill, the transport of powder from the bottom to thesurface might be reduced, thus leading to a less effective mixing during the roping regime. Thishypothesis is clearly confirmed by the observation of radial velocity component (Figure 11). It canbe seen, in particular for 40% mass fill and to a minor extent also for 30% mass fill, that radialvelocities becomes negative when a critical impeller speed is reached. According to the adoptedconvention the material on the surface moves towards the wall of the vessel, which is exactly theopposite of what happens at low velocity or low mass fill. These experiments therefore not onlystrengthen the conclusion of Plank et al. (2003) on the possible existence of stagnation period at thesurface for high fill levels but also show the possibility of having a reversal of the flow direction atthe surface. Also recent studies performed with a single blade moving in a granular bed confirmedthe possibility of significant changes in the flow profile and the absolute magnitude of the velocitieson the top of the particle by increasing the bed height (Radl et al, 2012). It is therefore suggestedthat a new regime, different from roping can progressively develop within the vessel with theformation of a two layered structure and the top layer “floating” or “surfing” over the bottom one. Itis hypothesized that such top layer, characterized by a low tangential velocity (~0.1 m/s) and anegative radial velocity at the surface, may constitute a second toroidal cell rotating in opposition tothat existing below. The free surface renewal as well as the overall bed renewal are expected to bepoor and impact negatively on the mixing efficiency in this regime. It has to be noted also that thisregime cannot be identified only by analyzing torque or motor current profiles, since they reach aplateau after the transition from bumping to roping regime.

Figure 12. Scheme representing the effects of mass fill and rotational speed on the transition between thedifferent regimes observed on the pilot-scale mixer.





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All the flow patterns and mixing regimes observed in this study have been qualitativelysketched as a function of impeller speed and mass fill in Figure 12. At low rotational speed bumpingregime dominates independently of the rotational speed, with convective recirculation zones in frontof the blades as described by Remy et al. (2010), which determine the periodic expansion of the bedat the surface. The influence of such recirculation zones on the surface flow pattern fades downincreasing the fill level. At higher rotational speed and low mass fill, the roping regime dominateswith the typical toroidal flow pattern. However, increasing the mass fill, a smooth transition occursand the bed splits in two portions: a bottom layer rotating according to the usual toroidal patternimposed by the blades and a surface layer with a motion almost independent of that close to theblades with the material “surfing” on the top and radially rotating in opposition to the bottom layer.

4 Conclusions

The main conclusions of this work can be summarized as follow: - a model for the prediction of theimpeller torque required to mix a cohesive powder mixture in a high shear mixer has beenproposed; - this new model has been used to plot experimental torque values in the form of a newdimensionless torque number against the square root of the impeller Froude number; - a static term,which mainly depends on the impeller clearance, and a dynamic term, which depends on the massfill, have been identified and their trends have been plotted against the Froude number; - this newmodel can be used to better explain and describe the powder flow behaviour during the high shearmixing. The model for torque prediction, developed at the bench-scale, has shown the major roleplayed by mass fill on the flow patterns. At pilot-scale, this specific aspect has been investigatedthrough motor current consumption and surface velocity measurements. It has been observed thatwhile torque profile can characterize the transition between the bumping and the roping regimes,the third regime here described can be captured only by surface observation and not by torque ormotor current profiles, since they both reach a plateau after the transition from bumping to ropingregime. Further experiments trying to characterize the extension of the observed surface convectivecells, as well as the variation in mixing efficiency due to the transition between the differentregimes need to be done in the future in order to complete the understanding of this mixing process.

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